[EM] Clone proofing Copeland
Chris Benham
chrisjbenham at optusnet.com.au
Sat Jan 6 13:22:26 PST 2007
Simmons, Forest wrote:
>Here's a version that is both clone proof and monotonic:
>
>The winner is the alternative A with the smallest number of ballots on which alternatives that beat A pairwise are ranked in first place. [shared first place slots are counted fractionally]
>
>That's it.
>
>This method satisfies the Smith Criterion, Monotonicity, and Clone Independence.
>
More not-so-good news for this Simmons method: it fails mono-raise
(aka Monotonicity).
31: A>B
02: A>C
32: B>C
35: C>A
C>A>B>C. "Simmons" scores: A35, B33, C32. C has the lowest score
and wins.
But if we raise C on the two A>C ballots, changing them to C>A, then we get:
31: A>B
32: B>C
37: C>A (2 of these were A>C)
C>A>B>C. "Simmons" scores: A37, B31, C32. Now B has the lowest
score and wins.
So raising C on some ballots without changing the relative ranking of
any of the other candidates has
caused C to lose, a failure of mono-raise.
Interestingly in both cases the method gave the same result as IRV. In
fact it is starting to look as
though in the 3-candidate case "Schwartz//Simmons" is equivalent to
Schwartz,IRV!
Say sincere is:
48: A
27: B>A
25: C>B
B is the CW, and in this case both methods (even without the "Schwartz"
component) elect B.
And both methods are vulnerable to the same Pushover strategy. If from 3
to 20 of the 48 A supporters
change their vote to C>A or C or even C>B, then both methods will elect A.
45: A
03: C>A (sincere is A)
27: B>A
25: C>B
B>A>C>B "Simmons" scores: A27, B28, C45. A has the lowest score
and so wins.
IRV eliminates B and likewise elects A.
28: A
27: B>A
45: C>B (20 of these are sincere A!)
B>A>C>B "Simmons" scores: A27, B45, C28. A has the lowest score
and so wins.
IRV eliminates B and likewise elects A.
Chris Benham
More information about the Election-Methods
mailing list